Question 980509: Good evening, I need a little help in my activity in trigonometry, about linear, angular speed and area of sector of circles, here's the problem.
The top and bottom ends of a windshield wiper blade are 34 in. and 14 in. from the pivot point, respectively. While in operation, the wiper sweeps through 135°. Find the area swept by the blade.
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
Using the formula:
Angle/360 = area of sector/πr^2
135/360 = area of sector/π 34^2
Cross multiply
360 x area of sector = 135 x π x 1156
Area of Sector = (135 x π x 1156)/360
Area of sector = 1361.88 ins^2
This is the large sector, now we estimate
the sector from 14 ins downwards
135/360 = area of sector/π x 14^2
Cross multiply
360 x area of sector = 135 x π x 14^2
Area of sector = 135 x π x 14^2/360
Area of sector = 230.91 ins^2
If you now take the area of the small sector
away from the area of the large sector, what
is left is the area swept by the blade.
1361.88 - 230.91 = 1130.97 ins^2
Hope this helps:-)
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